Dimensional analysis

Esme12, ASN, BSN, RN · Nov 16, 2013

here is an excellent site that explains dimensional analysis called Dave's easy calculations.....http://www.davesems.com/files/drug_dose_calculations.pdf

LoriRNCM, ADN, ASN, RN · Nov 16, 2013

Esme isn't that the fractional method? I think they also call dimensional analysis "Factor labeling" method.

Esme12, ASN, BSN, RN · Nov 17, 2013

Maybe I am of no help....here I thought it was dimensional analysis....It's how I figure drugs......here is a sheet for "dimensional analysis" http://www.siue.edu/nursing/slchs/pdf/dim_analysis_tutorial.pdf frankly I think they look the same.

Dimensional analysis: Calculate dosages the easy way

[h=3]Dimensional Analysis[/h]

https://www.dlsweb.rmit.edu.au/lsu/content/C_SET/nursing/nursingcalculations.html

I hope these help

LadyFree28, BSN, LPN, RN · Nov 17, 2013

To me, DA is the factoring/ratio proportion method EVOLVED. What helped me with dimensional analysis is to figure out what unit ( ml tab, mg, ml/hr, etc) is needed; before setting up the problem; I figure what is on hand, the order, and wanted, separately; for example:

Dose: 600 mg

Wanted: mL

On hand: 300 mg/mL

Once you "label" what is wanted, you ensure placement of what is wanted and isolate the value to make sure it is accurately factored; based on my example; the mL will be placed on numerator line and the 300mg will go on the denominator, successfully allowing the setup to look like this:

600mg |mL|

300 mg = ___mL

I am posting from my phone; so imagine the line horizontally; the mL is isolated as the wanted value amount.

Now, once the amount is calculated; you can reduce, OR calculate the value on hand; my rule of thumb is to calculate accordingly to avoid confusion or miscalculation; that is especially important in dealing with weight based calculations, IMHO. So, progressing along: the mg's are cancelled out, here is my additional setup:

600 mg | mL | 600

| 300| 300 = _____mL

So, including the horizontal line (again, typing on phone) division is needed to achieve the wanted value; this one's pretty straightforward; you can reduce and see the amount you need to give. :yes:

Do you have a DA book? It was required in my program to purchase a DA book. We used it throughout out program; it contained reconstitution problems, IV calculations, three step problems for complex problems for weight based and titration problems. I still use it to brush up on my DA, because I am very partial to ratio and proportion; however, I found DA to be more accurate in getting my answers than ratio and proportion, but that's me.

You can always look on YouTube, and there is a DA website as well-Esme has posted one of those in her post that is a great resource.

Hope this helps!

motay68 · Nov 18, 2013

To do DA you need to familiarize yourself with conversions. (e.g. g to mg or L to mL) My instructor taught us like this and I'm using the equation from esme's link.

You need to worry about two things: the starting label (Doc's order) and your answer label (what you have on hand) Set your equation up like this. SL (starting label)=AL (answer label)

If the Doc orders Gentamicin 55mg IM q8h

We have on hand 80mg/2mL

How many mL do we give to the patient? Round it to the nearest 10th

1. Factor out the junk of the problem. We are giving one dose. We (for the math portion) do not need to worry, unless it asks the route, how the med is given or how often the med is given. Cross out the IM and q8h. and even though the medication is important normally it isn't for the math portion. The only thing we need out of this equation for DA method is the amount the doc ordered and the amount we have on hand. So how do we get 55mg to turn into mL?

2. Our starting label is ALWAYS the order you receive from the doctor. So our starting label will be 55mg. Our answer label is ALWAYS what the question asks. In this case, how many mL's do we give to the patient?

Here is our set up so far

55mg=?mL Does this make any sense? No because mg and mL don't equal each other. and because they don't we may need to use some conversions to get them to make sense.

*On a side note: Don't throw up over conversions. I did because I suck at them, but they are really just rote memorization and a few of them are all you need.

Now really look at the order for the med and what we have in stock. The med is ordered 55mg. We have it in 80mg(mg=mg so no conversion necessary)/2mL

We don’t need conversion to figure this out because both the SL and AL are in mg

Here is how we should set up the problem to get the answer in mL

SL

55mg 2mL = mL

X 80mg

*bear with me. It’s a pain to do fractions in Microsoft Word.

The 2mL/55mg fraction is set up like that because of simple algebra. We need to get rid of everything on the left side of the equation that does not involve my answer label. Since my answer label is only concerned with mL’s I need to get rid of the mg. (following me? This is way more complicated to type out then say out loud. :lol2: ) Why do we set up our fraction with mL’s on top and mg’s on bottom? As per my nursing instructor (and basic algebra) nurses LOVE TO CROSS STUFF OUT!!!!!! Sooooo since we can only cross stuff out that are opposite each other (top vs. bottom) we can get rid of the mg’s because they cancel each other out

55 2mL = 110mL

X 80 80

Now all we need to do is divide 110 by 80 which equals 1.4 rounded to the nearest 10th. Then because the mL is the only part of the equation left after we divide the numbers we add that to the answer.

So we would give 1.4mL to the patient when we give the med.

If I have not completely confused you with this and it makes any sense, let me know and I’ll throw in a conversion so you can see how that is done too.

SimonTan · Nov 21, 2013

Dimensional analysis is SO FREAKING EASY that I don't even have to think about most questions. I write down the starting number and put in the conversion ration and BAM!, out comes the answer! No thinking involved.

Here's an example from my book(IV drip rates):

Pt ordered 120mg of Lasix. Available in liquid form 40mg/5mL.

So I write 120mg x 5mL/40mg = ? mL. I start out with 120mg and want to get to mL. The 5mL/40mg is the ratio so I flip it and multiply(you good with math I hope).

See how I flipped it? Because you want to cancel out the mg and be left with mL. Repeat. Cancel out mg because we want mL!

How can you just flip that? Check this out, since 1 hour = 60 minutes is a ratio(1hr/60min), isn't that basically = 1? So no matter how you flip it, it is still equal to 1! But what you want to do is cancel out the units(mg) to get to the units that you want(mL). It's like back in algebra a/b=c...in this case a(5mg) and b(40mg) are equal so a/b = 1. Remember, this is ratio given to you. And when they give you the ratio, that means a/b = 1. Like 1 teaspoon = 5mL, that's a ratio and it equals 1.

Now practice with your height convert to inches 1 foot = 12 inches.

Hope that helps, explanation could probably have been better.

Guests · Nov 21, 2013

Here's the crux of 'dimensional analysis' (which is a misnomer but so be it...)

A) Don't Eff with the equal sign

B) Multiplying/dividing both sides of an EQUATION does not Eff with the equal sign

C) Anything divided by itself is identically equal to one

D) Any two things which are equal to a third thing are also equal to each other

E) Item C applies to units just as well as it applies to numbers... if a dividend and a divisor are equal, they can be canceled.

F) Units may be multiplied and divided just as can numbers... don't believe me? What are the units of volume? cc = cubic cm = cm x cm x cm

~~~

I have to go now... this post to be continued...

Guests · Nov 22, 2013

Here's the crux of 'dimensional analysis' (which is a misnomer but so be it...)
A) Don't Eff with the equal sign
B) Multiplying/dividing both sides of an EQUATION does not Eff with the equal sign
C) Anything divided by itself is identically equal to one
D) Any two things which are equal to a third thing are also equal to each other
E) Item C applies to units just as well as it applies to numbers... if a dividend and a divisor are equal, they can be canceled.
F) Units may be multiplied and divided just as can numbers... don't believe me? What are the units of volume? cc = cubic cm = cm x cm x cm

The simplest 'dimensional analysis' problem is converting units.

Say they ask you to convert 170 lb into kilograms.

Start by writing an equation that relates the two units... that is, 1 kg = 2.2 lb

Keeping in mind that you can perform any operation that you'd like on one side of the equation just so long as it's replicated on the other side, you can divide each side by (1 kg) which yields 1 kg/(1 kg) = 2.2 lb/(1 kg) or...

2.2 lb / 1 kg = 1 ... or ... just 2.2 lb/kg... which is just 1

In words, this is just saying, "Two point two pounds per kilogram" or "If you have 2.2 pounds, it's the same as 1 kilogram"

Likewise, you can divide each side by (2.2 lb) which yields 1 kg/(2.2 lb) = 2.2 lb/(2.2 lb) or...

1 kg / 2.2 lb = 1

In words: "One kilogram per 2.2 pounds" or "If you have 1 kilogram, it's the same as 2.2 pounds."

Since both of these equations are identically equal to 1, and since you can multiply or divide anything by 1 and not change its value, you could multiply as follows...

170 lb x (2.2 lb / 1 kg)

Numerically, you'd get 374 but your units would square lbs per kg... which means... nothing...

Recognize, though, that you didn't CHANGE the value because you only multiplied by 1...

You could also multiply 170 lb by the inverse...

170 lb x (1 kg / 2.2 lb)

or, rearranging...

(170 lb / 2.2 lb) x 1 kg

or...

(170/2.2) x (lb/lb) x 1 kg

Numerically, you get 77.3... but what about your units? Now you have 'lb' in both the numerator and the denominator (that is, the dividend and the divisor are the same)... and "anything divided by itself = 1" so

(170/2.2) x 1 x 1 kg = 77.3 kg

You don't need to go through all of the preceding, though... all you need to do is start with your equality (for example, 1 kg = 2.2 lb), divide both sides by the same value to create a unit equality (for example, 2.2 lb/1 kg = 1) and then multiply by your unit equality or its inverse (2.2 lb/1 kg or 1 kg/2.2 lb) in order to cancel out the units that you're trying to convert...

In other words, just jump straight to:

170 lb x (1 kg / 2.2 lb) = (170/2.2) kg

More to come...

Guests · Nov 22, 2013

Here's the crux of 'dimensional analysis' (which is a misnomer but so be it...)
A) Don't Eff with the equal sign
B) Multiplying/dividing both sides of an EQUATION does not Eff with the equal sign
C) Anything divided by itself is identically equal to one
D) Any two things which are equal to a third thing are also equal to each other
E) Item C applies to units just as well as it applies to numbers... if a dividend and a divisor are equal, they can be canceled.
F) Units may be multiplied and divided just as can numbers... don't believe me? What are the units of volume? cc = cubic cm = cm x cm x cm

The simplest 'dimensional analysis' problem is converting units.
Say they ask you to convert 170 lb into kilograms.
Start by writing an equation that relates the two units... that is, 1 kg = 2.2 lb

Keeping in mind that you can perform any operation that you'd like on one side of the equation just so long as it's replicated on the other side, you can divide each side by (1 kg) which yields 1 kg/(1 kg) = 2.2 lb/(1 kg) or...
2.2 lb / 1 kg = 1 ... or ... just 2.2 lb/kg... which is just 1

In words, this is just saying, "Two point two pounds per kilogram" or "If you have 2.2 pounds, it's the same as 1 kilogram"
Likewise, you can divide each side by (2.2 lb) which yields 1 kg/(2.2 lb) = 2.2 lb/(2.2 lb) or...
1 kg / 2.2 lb = 1

In words: "One kilogram per 2.2 pounds" or "If you have 1 kilogram, it's the same as 2.2 pounds."
Since both of these equations are identically equal to 1, and since you can multiply or divide anything by 1 and not change its value, you could multiply as follows...
170 lb x (2.2 lb / 1 kg)

Numerically, you'd get 374 but your units would square lbs per kg... which means... nothing...

Recognize, though, that you didn't CHANGE the value because you only multiplied by 1...
You could also multiply 170 lb by the inverse...
170 lb x (1 kg / 2.2 lb)

or, rearranging...

(170 lb / 2.2 lb) x 1 kg

or...

(170/2.2) x (lb/lb) x 1 kg

Numerically, you get 77.3... but what about your units? Now you have 'lb' in both the numerator and the denominator (that is, the dividend and the divisor are the same)... and "anything divided by itself = 1" so

(170/2.2) x 1 x 1 kg = 77.3 kg
You don't need to go through all of the preceding, though... all you need to do is start with your equality (for example, 1 kg = 2.2 lb), divide both sides by the same value to create a unit equality (for example, 2.2 lb/1 kg = 1) and then multiply by your unit equality or its inverse (2.2 lb/1 kg or 1 kg/2.2 lb) in order to cancel out the units that you're trying to convert...
In other words, just jump straight to:

170 lb x (1 kg / 2.2 lb) = (170/2.2) kg
More to come...

There are several unit identities which you need to remember:

1 kg = 2.2 lb

1 kg = 1,000 g

(which also means that 1000 g = 2.2 lb)

1 min = 60 sec

1 hr = 60 min

1 day = 24 hr

1 Liter = 1000 mL

There are a bunch of others but these are the big hitters for most problems... except...

Drip factors...

For some reason, some people get freaked out by drip factors. I don't know why because drip factors are simply a reflection that some drops are bigger than are others.

You know this, of course, if you've ever been out in the rain. Sometimes the drops are tiny and you just get a little damp... other times, the drops are huge and you get soaked in the same amount of time...

IV tubing is made to produce uniform drops of the same volume... typically either 0.1 mL, 0.067 mL, or 0.017 mL. However, those are goofy numbers and we have no easy way to tell the volume of a drop so instead of speaking of "how many mL per drop," we rather speak of "how many drops per mL"...

Standard tubing is generally 10 drops per mL, 15 drops per mL, or 60 drops per mL

That is,

10 gtt = 1 mL or 10 gtt/mL

15 gtt = 1 mL or 15 gtt/mL

60 gtt = 1 mL or 60 gtt/mL

Another thing to recognize when doing word problems... the verb "to be" (e.g. is, were, are, will be) means "equals" in math terms... 'equals or not equals, that is the question'

OK, so let's do another simple example...

"The patient is on a Protonix drip at 8 mg/hr. If it's stopped after 15 minutes, how much drug did the patient get?"

8 mg/hr x (1 hr = 60 min) x (15 min)

The question is, should the middle term be written as (1 hr/60 min) or as (60 min/1 hr)?

Try it both ways... they're both valid because they both equal one... but one way gives goofy units, one way gives the units that you're looking for... "mg"

If you write it as (1 hr/60 min) then you have (hr/hr) and (min/min) meaning they cancel to leave only mg as your units

The answer is [2 mg]

OK, another example...

"Your septic patient is due a 1 gram of Vancomycin which comes premixed in a bag containing 200 milliliters of solution. Because the patient has very fragile veins, the physician and the pharmacist agree that the medication should run slowly over 90 minutes while co-infusing with NS.

(i) You are a nurse who eats your young (they're quite soft and tasty) so, to keep the nursing student out of your hair, you assign them to count the total number of drops. How many should they count? (assuming your tubing was already primed w/ NS)

(ii) At what rate (in mL per hr and mL per minute) should it run?

(iii) Using 15 gtt tubing, how many drops should you count in 15 seconds?

(iv) Your nursing student was trying to dazzle you with his knowledge that Vanco is supposed to run over an hour and dutifully shut off the pump after 60 minutes. How much more Vanco, in milligrams, does the patient need?

First, find your unit identities:

1 gram = 200 mL (How much Vanco is in the bag? 1 gram... How much solution is in the bag? 200 mL)

15 gtt = 1 mL

1 min = 60 sec

1 hr = 60 min

(i) How many drops does it take to make up 200 mL?

200 mL x (1 mL = 15 gtt)... Which one: (1 mL/15 gtt) or (15 gtt/1 mL)

Try 'em both and see which one gives you an answer in gtt

(ii) 200 mL over 90 minutes

200 mL / 90 minutes = 2.2 mL/min

How 'bout mL/hr?

200 mL / 90 min x (1 hr = 60 min)... which one: (1 hr/60 min) or (60 min/1hr)?

133 mL/hr

(iii) 200 mL / 90 minutes x (15 gtt = 1 mL) x (1 min = 60 sec)

which ones make the units work out?

(15 gtt/1 mL) or (1 mL/15 gtt)?

(1 min/60 sec) or (60 sec/1 min)?

0.556 gtt/sec x 15 sec = 8 drops in 15 seconds

(iv) At the set rate, how much Vanco went in over 60 minutes?

(1 g = 90 minutes) x 60 min x (1 g = 1000 mg)

Which ones?

(1 g/90 min) or (90 min/1 g)

(1 g/1000 mg) or (1000 mg/1 g)

It doesn't matter which one... they're both valid (that is, both equal 1)... you just need to invert as needed so that you end up with like units in the numerator and the denominator thus canceling

Dose given: (1 g/90 min) x 60 min x (1000 mg/1 g) = 667 mg

Additional needed: 1000 - 667 = 333 mg

{How many mL is that? (200 mL / 1000 mg) x 333 mg = 67 mL

~OR~

(90 min/1 g) x (1/60 min) x (1 g/1000 mg) = 0.0015/mg

But, you say, in the second one, the units don't work...

But, I reply, they do... you just need to invert... since all you're doing in all of this is multiplying and dividing by 1... you get to invert as much as you want without changing anything.

1/(0.0015/mg) = 667 mg

Guests · Nov 22, 2013

Why does this matter?

You might find yourself in the position I did 2 shifts back... in a room with a 3rd year resident and 2 our most senior attendings and the assistant nurse manager and another one of our top-flight nurse when...

The doc hands me a bag of meds and says, "give her 12 mg of etomidate now. We'll shock her twice. If she doesn't convert, we're going to intubate with 24 of etomidate and 140 of roc." I'm looking down at two vials of etomidate which are labeled 40 mg/20 mL.

How much do I give the first dose?

How much the second?

No pen, no paper... and no time. I either do it, and do it right... just like the docs do... or I hand it over to somebody else and step back out of the way.

40 mg per 20 mL means 2 mg per 1 mL which means 12 mg per 6 mL and 24 mg per 12 mL.

I pulled up 6 mL in one syringe and 12 mL in the other syringe.

I do my thing, the doc tubes her, and I take care of her for the next several hours until I wheel her up to the ICU... My patient from the time she rolled in the door until I handed her off to the unit.

LoriRNCM, ADN, ASN, RN · Nov 23, 2013

Awesome awesome awesome!!!!!!!!!!!!! Thank you all!!!!!!!!!!